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INVESTIGATION AREAS & PERIMETERS
This investigation looks at the connection between the area and the perimeter of a rectangle.
All diagrams are not to scale. The sides of all rectangles are whole numbers.
(a) Find the area of this rectangle.
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Some rectangles have area 4.
There are three ways to calculate their area.
[Table_1]
(b) Some rectangles have area 6.
There are four ways to calculate their area.
Complete the table below to show all four ways.
The first one has been done for you.
[Table_2]
(c) Some rectangles have the same area.
(i) There are exactly two ways to calculate their area.
Complete the table when this area is a number between 6 and 15.
[Table_3]
(ii) There are exactly three ways to calculate their area.
Complete the table when this area is a number between 6 and 15.
[Table_4]
(iii) There are more than four ways to calculate their area.
Complete the table when the area is a number between 6 and 15. You may not need all the lines.
[Table_5]
565
561
583
Some rectangles have the same area. This area is between 1 and 20.
(a) (i) List the areas that can be calculated in exactly two ways.
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(ii) Write down the mathematical name for the numbers in your answer to part (a)(i).
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(b) (i) List the areas that can be calculated in an odd number of ways.
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(ii) Write down the mathematical name for the numbers in your answer to part (b)(i).
...............................................................................
510
517
574
Some rectangles have the same area. This area is between 150 and 200.
Find an area that can be calculated in an odd number of ways.
521
530
546
The perimeter of this 4 by 5 rectangle is 18.
[Image_1: Rectangle with width 4 and height 5]
Find the perimeter of each of these rectangles.
[Image_2: Rectangle with width 10 and height 3]
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[Image_3: Rectangle with width 9 and height 2]
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571
563
585
The width of a rectangle is 3.
Its area and its perimeter have the same value.
(a) Find its length.
(b) Write down its perimeter.
529
505
572
(a) Write down an expression for the area of this rectangle.
(b) Write down an expression for the perimeter of this rectangle.
(c) The area and the perimeter have the same value.
Write down an equation and solve it to find $x$.
544
564
539
A rectangle has width 2 and length $x$.
Show that this rectangle cannot have the same value for its area as its perimeter.
597
597
568
